Relation between Cultivar and Keeping Quality for Batches of Cucumbers
R.E. Schouten, L.M.M. Tijskens
and O. van Kooten
Horticultural Production Chains,
Wageningen University,
Wageningen, The Netherlands
G. Jongbloed
Division of Mathematics and Computer
Science,
The Vrije Universiteit,
The Netherlands
Keywords: Biological variation, postharvest, preharvest, precursor, mathematical
approach
Abstract
This paper focuses on the characterisation of the cultivar effect in batches
with respect to batch keeping quality based on colour measurements only. To do so,
a correction for the maturity per batch had to be made for two batches per cultivar.
This left the cultivar information with respect to the batch keeping quality. This
method to extract cultivar information out of cucumber batches is shown for six
batches from three cultivars (‘Volcan’, ‘Beluga’ and ‘Borja’) over two growing
seasons. The method consist of describing the batch keeping quality determining
property on an individual level and then translating it to a batch level, thereby
introducing and describing biological variation. It turned out that the best cultivar,
with respect to batch keeping quality, was ‘Borja’, followed by ‘Beluga’ and finally
‘Volcan’. This paper demonstrates how to use the biological variance present in all
biological batches; to take advantage of the biological variation instead of seeing and
dealing with it as if it were a nuisance.
INTRODUCTION
On first sight, it seems impossible to recognise whether fresh cucumbers are from
the same cultivar. Still, cucumber-breeding companies have sometimes large programs to
develop new populations with genetically distinguishable properties. Those properties
may well be keeping quality or resistance against pests. This paper focuses on the
characterisation of the cultivar effect with respect to keeping quality.
The limiting quality attribute for cucumbers is colour (Schouten et al., 1997). The
keeping quality can be defined as the time it takes for an individual cucumber to reach a
predefined colour limit. Long shelf life of cucumbers has been associated with high
chlorophyll content in the peel (Lin and Jolliffe, 1995). However, it is known that
cucumbers of the same colour can exhibit large differences in colour upon reaching the
customer. So, for a high keeping quality, not only the initial colour is of interest, but also
specifically the ability to stay green. For individual cucumbers this is not possible,
because of the unknown stage of maturity (Schouten et al., 1997). However, this is
different when batches (one grower, one harvest and of the same cultivar) of cucumbers
are considered. On a batch level, next to information on all individuals belonging to that
batch, extra information is available due to the shared harvest date, cultivar and grower.
Batch keeping quality can be defined as the time it takes before 5% of the cucumbers in a
batch reaches the predefined colour limit (Schouten and Van Kooten, 1998).
This paper focuses on the characterisation of cultivar effects with respect to batch
keeping quality from a modelling point of view. Models will be presented on two
aggregation levels. The first level is on the level of the individual cucumber, the second is
the batch level which describes the batch itself, but also a cultivar dependant parameter.
All models are based on non-destructive, repeated measurements, of colour. The models
will be applied to six batches of cucumbers from three cultivars over two growing
seasons.
Proc. Postharvest Unltd
Eds. B.E. Verlinden et al.
Acta Hort. 599, ISHS 2003
451
MATERIAL AND METHODS
Cucumbers
Cucumbers consisted of six batches of 80-100 cucumbers each, belonging to either
cultivar ‘Volcan’, ‘Borja’ or ‘Beluga’, obtained from the Almeria region in Spain. Three
batches were harvested in September 1998 (autumn season) and three batches were
harvested in June 1999 (spring season). All batches were grown under equal, commercial
growing conditions and were of marketable size and colour. After harvest, batches were
placed in boxes with air-filled polystyrene and transported to the measuring facility in the
Netherlands within 24 hours. Upon arrival cucumbers were individually tagged on the
lightest side and stored in the dark at 20 °C and 100% RH.
Colour Measurements
Image analysis was used for colour measurements using a JVC KY-F30 3CCD
colour video camera, with the same set-up as described in Schouten et al. (1997). Colour
measurements per cucumber took place twice per week and were expressed as the ratios
of the blue/red (B/R) values from the separate intensities of the blue and red values of the
RGB colour scale. After a measurement, the light intensities for the red and blue colour
were separately averaged over all pixels that belong to the cucumber image. Colour
measurements started one day after arrival at the measuring facility and ended when
yellowing was complete or decay of the cucumber was imminent.
Colour Behaviour of Individual Cucumbers
The colour model is based on knowledge obtained from literature regarding the
processes of synthesis and degradation of chlorophyll in terms of colour compounds.
POR (protochlorophyllide oxidoreductase) is a photo-enzyme which catalyses the
reduction from protochlorophyllide (Pchl) to chlorophyllide (chl), the direct precursor of
chlorophyll (CHL) (Lebedev and Timko, 1998). A ternary complex of POR:NADPH:Pchl
has been observed, which may be assumed to be a safe form of Pchl storage as to prevent
photo-toxic events when illuminated during the initial greening of young tissues (Porra,
1997). Here the assumption is made that the concentration of the complex
POR:NADPH:PChl formed during pre-harvest is restrictive for the concentration of chl
and CHL formed during postharvest.
During senescence in fruits and vegetables chlorophyll can be cleaved by
chlorophyllase resulting in the formation of chl, which will be turned into colourless
compounds (Heaton and Marangoni, 1996).
From a modelling point of view, only compounds with colour and their precursors
are of interest. Next to CHL itself (blue green), this is chl (blue green), and the colourless
precursor Pchl. Colour is defined as the sum of CHL and chl. Fig. 1 shows the proposed
mechanism for these compounds during synthesis and breakdown of CHL. chl holds a
special position as it is an intermediate in both synthesis and breakdown. The initial
concentration of Pchl, as part of the ternary complex POR :NADPH:PChl, is depicted as
crucial and governing the colour behaviour.
The mechanism shown in Fig. 1 can be expressed in mathematical form by
coupled differential equations, one for each process (Schouten et al., 2002). These
equations were solved analytically which resulted in a model formulation describing
colour behaviour from harvest time till complete yellowing of an individual cucumber in
terms of Pchl0 and CHL0, with Pchl0 and CHL0 being the concentration of Pch and CHL
present at harvest time (Schouten et al., 2002).An indication of the colour behaviour in
time decay for three hypothetical cucumbers, differing only in Pchl0, is depicted in Fig 2.
The colour model does not contain or need cultivar factors.
Keeping Quality of Batches of Cucumbers
Batch keeping quality was determined for the six batches of cucumbers. First the
colour data per cucumber, obtained by following the colour development in time by
452
repeatedly measuring the same cucumbers with image analysis, were analysed with the
colour model to estimate the values of Pchl0 and CHL0 per cucumber. Then, the time it
took for each cucumber to reach the colour limit was determined using the estimates of
Pchl0 and CHL0. To obtain the batch keeping quality the keeping qualities of all
cucumbers in a batch were sorted on time. When necessary, a simple linear interpolation
procedure was used to estimate the time at which 5% of individuals in that batch crossed
the colour limit (Schouten et al., 2002). Batch keeping quality depended on season and
cultivar, ‘Borja’ having the highest and ‘Volcan’ having the lowest keeping quality (Table
1). As expected, the average concentration of Pchl0 per batch was closely related to the
batch keeping quality (Table 1).
Behaviour of Pchl during pre- and postharvest for Individual Cucumbers
During postharvest Pchl is broken down into chl according to the mechanism
shown in Fig. 1. During preharvest Pchl is thought to be stored in the ternary complex
POR:NADPH:Pchl and subsequently released when exposed to light (Porra, 1997). The
behaviour of Pchl may be described as a consecutive reaction where Pchl as part of the
ternary complex (PT) is transformed into Pchl, and the subsequent decay of Pchl. From
this proposed mechanism, the behaviour of Pchl over time can be extracted using the
fundamental rules of chemical kinetics. The set of differential equations is given in Eq. 12.
∂ PT
= − k ⋅ PT
(1)
T
∂t
∂ Pchl
= k ⋅ PT - k ⋅ Pchl
T
f
∂t
(2)
where kT is the reaction rate for the formation of Pchl from PT. This set of differential
equations can be solved analytically for constant external conditions. Given that no Pchl
was present at the start of the cucumber growth, Pchl can be expressed as follows (Eq. 3).
where PT0 is the initial concentration of PT present at the start of cucumber growth. An
−k ⋅t
-k ⋅t
⋅ PT (−e T + e f )
0
Pchl(t) = T
(3)
k −k
T
f
indication of the behaviour of Pchl in time may now be simulated for different
cucumbers, each differing in PT0 and assuming a constant temperature during pre- and
k 
ln T 
k 
(4)
t
=  f 
max k − k
T
f
postharvest. Surprisingly, the maximum in Pchl occurs at tmax independently of PT0 (Eq.
4).
tmax depends only on the reaction rate constants kf and kT. During the analysis of the colour
data of cucumbers calibrating the postharvest colour model it was observed that all
reaction rate constants were identical for a number of cultivars (Schouten et al., 2002). It
may be assumed that, next to kf, kT does not show much difference between cultivars. In
that case PT0 is determinant for the behaviour of Pchl in time and tmax will be constant for
all cucumbers, irrespective of cultivar, when cucumbers are grown at the same
temperature.
As very young cucumbers already show considerable amounts of greening it may
be assumed that the ternary complex POR:NADPH:Pchl can be quickly transformed into
k
453
Pchl. Therefore, when full-grown cucumbers are harvested it is likely that the
concentration of Pchl is already decreasing. Harvest probably takes place somewhere in
the range between tmax and t=+∞. When the behaviour of Pchl is observed for t ≥ tmax then
the behaviour shows similarities with a decreasing logistic function varying between 0
and Pmax. This logistic function can be expressed as follows (Eq. 5):
Pchl(t) ≈
P
max
P
k⋅t
mat
1 + e max
(5)
with
t max ≤ t mat ≤ ∞
where Pmax is defined as the concentration of Pchl at t= tmax. Pmax is assumed to be cultivar
specific. By using the logistic function for Pchl(t) instead of Eq. 3 a time transformation is
introduced. In Eq. 3, t stands for the time from the start of cucumber growth, but in Eq. 5
it had been replaced by tmat, the maturity of a cucumber. tmat varies between -∞ and ∞. At
tmat= -∞ the optimal maturity is reached as it is equivalent to the concentration of Pchl at
tmax (Pmax) and at tmat= ∞ the minimal maturity is reached as at that point no Pchl is left.
When no Pchl is left the cucumber will start to lose colour quickly (Fig. 2).
Behaviour of Logistic Batches in Time
As Pchl plays also a decisive role in the batch keeping quality, it is of interest to
know how the behaviour of batches in time is with respect to the Pchl concentration. To
do that the concept of biological variation has to be used. This might be defined as the
composite of (biologically based) properties that differentiate individual units of a product
(Tijskens and Konopacki, 2001). Here, it is proposed that biological variation can be
applied on the level of tmat. This means that a batch can be characterised by variation in
tmat, indicated by tmatb with standard deviation σ.
The connected open symbols of Fig. 3 show the distributions of all individual
values of Pchl0 gathered per batch. Those distributions are shown as function of a class of
Pchl0 and expressed as frequency, the fraction of cucumbers in that class. To describe this
mathematically, a description has to be given of the probability that a faction of the batch,
represented by Pchlb, is within a specific class (Eq. 6).
) ∈ (q , q ]) = Pr  Pchl b (t
) ≤ q  − Pr  Pchl b (t
) ≤ q 
(6)
mat
0 1
mat
1
mat
0



where q0 and q1 are used to describe the class borders, expressed in Pchl values. The aim
is to translate batch function Pchlb in terms such as tmatb, σ and Pmax. This translation
involves a small number of mathematical steps which are omitted here for clarity (Eq. 7).
b  - ψ Pchl - 1 (q ) − t
b 
Pr(Pchl b (t
) ∈ (q , q ] = ψ Pchl - 1 (q ) - t
(7)
mat
0 1
0
mat
1
mat

 

Pr(Pchl b (t
Ψ stands for the cumulative distribution function which describes the variation in tmat. The
next step is to choose which mathematical description should be used for Ψ. In Fig. 3 the
Pchl0 values are expressed as faction of all cucumbers that belong to a batch, i.e. values
between 0 and 1, so for Ψ a normalised function should be chosen. Out of convenience it
was assumed that Ψ was normally distributed. The probability that a faction of the batch,
represented by Pchlb, is within a specific class can now be expressed in terms of Pchl,
tmatb, σ and Pmax, the cultivar specific parameter, when the approximated (inverse) version
of Pchl (Eq. 5) is substituted (Eq. 8).
454
   q − Pmax 
  q − Pmax 


 ln − 0

1
-t


b
ln b
−t
 


mat

mat


q
q
0
1




b


 (8)

Pr(Pchl (t
) ∈ (q , q ] = Φ
-Φ


mat
0 1


k ⋅ Pmax ⋅ σ
k ⋅ Pmax ⋅ σ
 


 



 

with Φ the normalised cumulative normal distribution function. An indication of the batch
behaviour for one batch varying in maturity is shown in Fig. 4.
RESULTS AND DISCUSION
Shape of Distributions
The autumn batches of cultivars ‘Beluga’ and ‘Volcan’ show the skewed
distributions for batches which have almost the minimum Pchl0 concentration. On the
other hand the distribution of the spring batch of cultivar ‘Volcan’ shows also a skewed
distribution (but mirrored) typically for a batch which has almost the maximum
concentration of Pchl0. The shape of the distributions varies between two limits in which
vicinity they are skewed. Between those limits the distribution adopts almost the shape of
the normal distribution, for instance for the autumn batch of cultivar Borja. The first limit
is the one at a value of 0 for Pchl0 and the second limit at a maximum value of Pchl0. This
maximum value, Pmax, may be specific for each cultivar.
Estimation of Pmax
Fig. 3 shows the Pchl0 distribution per batch estimated on colour data (connected
open symbols) and analysed using the logistic batch model formulation of Eq. 8 (closed
symbols). Distributions of all batches were analysed in one optimalisation to obtain the
logistic rate k over all batches, Pmax per cultivar, tmaxb and σ per batch (Table 1). The nonlinear regression routine of Genstat (release 3.2, Lawes Agricultural trust, Rothamsted
Experimental Station, UK.) was used. Genstat has a convenient standard function build in
for Φ.
For cultivar ‘Volcan’, σ varied substantially over the growing seasons, while this
was not the case for both other cultivars (Table 1). Only during the spring season for
cultivars ‘Volcan’ and ‘Borja’ positive tmatb were encountered. This means that, compared
to the other batches, these batches were of much better maturity. When only σ and tmatb
are concerned, the spring batch of cultivar ‘Volcan’ is the best batch. However, the
influence of Pmax, which is the largest for cultivar ‘Borja’ and the smallest for cultivar
‘Volcan’ (Table 1, Fig. 3) is substantial. When a correction for maturity and σ per batch is
carried out, the best cultivar with respect to batch keeping quality is ‘Borja’, followed by
‘Beluga’ and finally ‘Volcan’.
Biological Variation
Normally, biological variation is treated like an ever present nuisance which
should be minimised as much as possible. Most commonly used technique to deal with
biological variation is sorting and grading on external quality attributes (Tijskens and
Konopacki, 2001). Simple colour measurements on cucumber colour are, however, not
enough for keeping quality predictions as the ability to stay green cannot be assessed. For
cucumbers it turned out that the precursor of colour components was determining batch
keeping quality. Building in biological variation on the level of tmat of the precursor
function might be possible for a host of other products, provided that process-based
models are available or can be generated to describe the behaviour of the quality attribute
and the precursor. In this paper the first practical application on how to take advantage of
the biological variation is presented.
455
One problem exists applying this biological variation incorporation technique. The
function describing the behaviour in time of the precursor (Eq. 3) needs to be
continuously increasing or decreasing, otherwise the inverse does not exist. This inverse
is needed when incorporating process based information into the batch model (Eq. 7).
Likely, most process-based descriptions in physiology do not comply with this condition.
Therefore a way to circumvent this condition had to be made by transforming the exact
Pchl function (Eq. 3) to an approximated version (Eq. 5).
Literature Cited
Lebedev, N., Timko, 1998. Protochlorophyllide photoreduction. Photosynthesis research
58, 5-23.
Lin, W.C., Jolliffe, P.A. 1995. Canopy light effects shelf-life of long English cucumber.
HortScience 26, 1299-00.
Porra, R.J. 1997. Recent progress in porphyrin and chlorophyll biosynthesis. Photochem.
photobiol. 65, 492-516.
Schouten, R.E., Otma, E.C., van Kooten, O., Tijskens, L.M.M. 1997. Keeping quality of
cucumber fruits predicted by the biological age. Postharvest Biol. Technol. 12, 175181.
Schouten, R.E., van Kooten, O. 1998. Keeping quality of cucumber batches: Is it
predictable? Acta Hort. 476, 349-355.
Schouten, R.E., L.M.M. Tijskens, L.M.M. and van Kooten, O. Predicting keeping quality
of batches of cucumber fruits based on a physiological mechanism. Postharvest Biol.
Technol. (in press).
Tijskens, L.M.M. and Konapacki, P. 2001. Biological variance in agricultural products.
Theoretical considerations. Proc. 8th International Controlled Atmosphere Research
Conference CA2001, Rotterdam, The Netherlands 8-13 July (in press).
Tables
Table 1. Overview of parameters belonging to the six batches. k and Pmax are common for
all batches and per cultivar, respectively.
cultivar
season
‘Volcan’
‘Volcan’
‘Borja’
‘Borja’
‘Beluga’
‘Beluga’
autumn
spring
autumn
spring
autumn
spring
R2adj (%)
n
93.2
282
456
batch keeping
k average
sigma
quality (days)
Pchl0 estimate
s.e.
3.8
0.11
23.34
2.12
6.8
0.59
4.959
2.31
13.77
1.12
8.4
0.69
0.024
15.59
1.20
13.1
1.54
7.466
1.55
4.3
0.12
6.757
1.46
7.2
0.65
tbmat
estimate
s.e.
30.09
1.06
-6.87
3.86
7.99
1.17
-6.76
3.08
28.502 0.633
5.06
2.74
Pmax
estimate
s.e.
1.752
0.106
2.869
0.194
2.230
0.204
Figurese
Pchl
kf
chl
kd
kfw
CHL
kbw
colourless
Colour value (blue/red)
Fig. 1. Model representation of the last part of the chlorophyll pathway for cucumbers
stored in the dark. Closed arrows indicate chlorophyll synthesis and open arrows
catabolism. Indicated are the reaction rate constants.
colour limit
Pchl0=2
Pchl0=1
Storage time (days)
Fig 2. Colour behaviour for of three cucumbers differing in Pchl0. Indicated is the colour
limit. The cucumber with the smallest concentration of Pchl0 has an intercept with
the colour limit at 0, the medium concentration at 8and the highest concentration
at 20 days. This intercept is defined as the keeping quality for individual
cucumbers.
457
cultivar ‘Volcan’
0.4
Pmax
frequency/probabillity
0.5
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
2
2.5
3
2.5
3
Pchl 0
cultivar ‘Borja’
0.4
0.3
Pmax
frequency/probabillity
0.5
0.2
0.1
0
0
0.5
1
1.5
Pchl0
cultivar ‘Beluga’
0.4
0.3
0.2
Pmax
frequency/probabillity
0.5
0.1
0
0
0.5
1
1.5
2
Pchl 0
Fig 3. Distribution of Pchl concentrations at harvest (Pchl0) for two batches per cultivar.
Per cultivar one batch was harvested in the autumn season (□,■) or the spring
season (◊,♦). Open symbols indicate the Pchl distribution obtained from colour
data, closed symbols the distribution from batch model estimations.
458
tmatb= 20
tmatb= -20
tmatb= 16
tmatb= -16
tmatb= 12
tmatb= -12
tmatb= 8
tmatb= -8
tmatb= 4
tmatb= -4
tmatb= 0
Fig. 4. Simulation of Pchl distributions for one batch harvested at different maturity
stages, indicated by tmatb. Simulation was carried out using Pmax =1, k=0.15 and
σ=5, applying Eq. 8.
459